Zero forcing 2-hop domination of graphs / Decemae Joy A. Arnante, Angelica D. Mora, and Mary Joy A. Ramboyong.

Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026.

Includes bibliographical references.

This study investigates zero forcing 2-hop domination in graphs, a graph param- eter that integrates the propagation mechanics of zero forcing with the coverage requirements of 2-hop domination. A set Z ⊆ V(G) is a zero forcing 2-hop dominat- ing set of a graph G if Z is both a zero forcing set and a 2-hop dominating set. The zero forcing 2-hop domination number is the minimum cardinality of Z, denoted by γz2h(G). This paper formally establishes results on the zero forcing 2-hop domi- nation numbers of various classes of graphs, including paths Pn (n ≥ 5) and cycles Cn (n ≥ 5), where both values are determined by n (mod 4). Moreover, the zero forcing 2-hop domination numbers on complete graphs Kn (n ≥ 5), complete bipar- tite graphs Km,n (m, n ≥ 3), and wheel graphs Wn (n ≥ 6) are also established. The results of γz2h(G) are similar to parameters like zero forcing hop domination. Fur- thermore, conjecture on the zero forcing 2-hop domination number of the tadpole graph, where n ≥ 3, is presented.